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Elanso
3 months ago
13

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby’s s

old the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Business
1 answer:
Nady [3.6K]3 months ago
6 0

Response:

The yearly return on the investment in this sculpture is -4.46%.

Details:

Let PV represent the investment amount, while FV is the value after t periods.

FV = PV(1+r)^t

(1+r)^t = FV/PV

1 + r = (FV/PV)^(1/t)

r = (FV/PV)^(1/t) - 1

Here, t is the duration from 1999 to 2003, so t = 2003 - 1999 = 4 years.

FV is $10,311,500.

PV is $12,377,500.

  r = ($10,311,500/$12,377,500)^(1/4) - 1

  r = -0.0446

Consequently, his yearly rate of return on the sculpture is -4.46%.

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Answer:

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Year          Pre-tax         GAAP Tax-  Tax Taxable   Income Tax      Deferred

          GAAP Income  able Income    Income      Payable Expense  Liability

                  (a)                     (b)                (c)             25%       25%   (Recovery)

                                                                                of (c)      of (b)  

2020     $230,000      $200,000     $110,000  $27,500 $50,000  $22,500

2021        250,000        220,000      250,000    62,500   55,000     (7,500)

2022       240,000         210,000      240,000    60,000   52,500     (7,500)

2023       240,000         210,000      240,000    60,000   52,500     (7,500)

Total     $960,000      $840,000    $840,000  $210,000 $210,000      0

Explanation:

a) Data and Calculations:

Cost of the depreciable asset = $120,000

Estimated useful life = 4 years

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GAAP depreciation expense = 25% for 2020, 2021, 2022, and 2023

Tax rate for each year = 25%

Year          Pre-tax         GAAP Tax-  Tax Taxable   Income Tax      Deferred

          GAAP Income  able Income    Income      Payable Expense  Liability

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                                                                                of (c)      of (b)  

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2023       240,000         210,000      240,000    60,000   52,500     (7,500)

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